Place the raw cashews in a small bowl of hot water to soak for 15 minutes, then drain.
Bring a large pot of salted water to a boil and cook the chickpea pasta according to package instructions.
During the last 3 minutes of pasta cooking, add the broccoli florets to the same pot to blanch until tender-crisp.
In a high-speed blender, combine the drained cashews, firm tofu, nutritional yeast, lemon juice, lemon zest, garlic powder, onion powder, sea salt, black pepper, and 0.25 cup of fresh water.
Blend the sauce ingredients on high until completely smooth and creamy.
Drain the pasta and broccoli, then return them to the pot over low heat.
Pour the creamy vegan cheese sauce over the pasta and broccoli, tossing gently to coat until heated through.
Serve immediately, garnished with an extra pinch of black pepper if desired.